Stability of General Cubic Mapping in Fuzzy Normed Spaces

We establish some stability results concerning the general cubic functional equation f (x + ky) - kf (x + y) + kf (x -y) - f (x - ky) = 2k( - 1)f (y) for fixed k∈ N-{1} in the fuzzy normed spaces. More precisely, we show under some suitable conditions that an approximately cubic function can be approximated by a cubic mapping in a fuzzy sense and we establish that the existence of a solution for any approximately cubic mapping guarantees the completeness of the fuzzy normed spaces.

Keywords:

Generalized Hyers-Ulam-Rassias stability , Cubic functional equation , Fuzzy normed spaces